Aren't there some American Eagle flights in the Caribbean that link one non-US island to another non-US island?

MVD-EZE is the only other market that comes to mind. UA recently pulled out of that market, but the fares are fairly low on AA. There are even specific AAdvantage awards for this market.

UA and NW have far more extensive fifth freedom flights in Asia, mainly over Hong Kong and Tokyo. In many cases, travelers from the US represent only a tiny fraction of the passengers.